The present invention relates to a method for measuring cross-relation rates in high-resolution nuclear magnetic resonance (NMR) spectroscopy in which in a homogeneous static magnetic field B.sub.0 in direction of a z-axis which causes alignment of longitudinal components I.sub.Z.sup.A, I.sub.Z.sup.X of magnetization vectors I.sup.A, I.sup.X of nuclei A, X during a time interval .tau..sub.m a sample substance, preferably dissolved in liquid, with nuclei A and X having different chemical shifts .OMEGA..sub.A and .OMEGA..sub.X is irradiated with a radio-frequency (rf) field and afterwards by action of a suitable rf-pulse sequence the longitudinal magnetization is transferred into a transverse magnetization creating a rf-signal received by a detector.
Such a method is known from the textbook by D. Neuhaus and M. P. Williamson, The Nuclear Overhauser Effect in Structural and Conformational Analysis, Verlag Chemie, 1989.
Ever since Solomon's celebrated work it has been obvious that the measurement of cross-relaxation rates may provide a unique approach to the determination of internuclear distances in solution. Cross-relaxation, also referred to as the Overhauser effect, leads to a partial exchange of longitudinal magnetization components I.sub.Z.sup.A and I.sub.Z.sup.X. The rate of this process is in principle proportional to the inverse sixth power of the internuclear distance r.sub.AX. However, the trouble with cross-relaxation phenomena is that they are easily perturbed by the presence of further spins. For example, if there is a third spin M such that r.sub.AM and r.sub.MX are both smaller than r.sub.AX, the conversion of I.sub.Z.sup.A into I.sub.Z.sup.X via I.sub.Z.sup.M will be much faster than the direct exchange of I.sub.Z.sup.A and I.sub.Z.sup.X, so that the measurement of the distance r.sub.AX becomes unreliable. Only in isolated spinpairs can one hope to measure distances with reasonable accuracy. In larger spin systems, the initial rate approximation is often invoked to justify the use of the two-spin approximation. Although this approximation is certainly acceptable for dominant interactions, it cannot be applied to weaker long-range Overhauser effects that tend to be overshadowed by stronger interactions.
Therefore, it is an object of the present invention to circumvent the fundamental difficulties described above and to present a method for measuring cross-relaxation rates which can still be used in those cases where the normal nuclear Overhauser effect in the laboratory-frame is perturbed by the presence of further spins.
This object is achieved by the present invention in that the rf field is composed by at least two weak, selective component fields, the frequencies of these fields being chosen such that the magnetization vectors I.sup.A and I.sub.X are made to nutate in synchronous fashion, the remaining spins of the sample substance substantially being unaffected by this process.
The nuclei are irradiated simultaneously with the sidebands of an usually amplitude-modulated rf field, so that their magnetization vectors are synchronously forced into a nutation movement. While the magnetization of the two selected nuclei A and X in a molecule are being stirred in this manner, cross-relation between the nuclear spins can occur in a manner that closely resembles the exchange in the laboratory-frame described by Solomon's equations. Suitably prepared initial conditions lead to simple exponential decays. The cross-relaxation rates may then be derived from the difference of the decay rates. Internuclear distances between selected nuclei may then be derived from these cross-relaxation rates, and this even in cases where normal Overhauser effects are perturbed by the presence of further spins.
The simplest realization of the method according to the present invention assuming that there is no weak coupling J.sub.AX between the spins of the nuclei A and X is that the amplitudes and the frequencies of the component fields are chosen such that together they form an amplitude-modulated rf field in direction of a y-axis orthogonal to the z-axis with a carrier frequency .omega..sub.rf =1/2 (.OMEGA..sub.A +.OMEGA..sub.X) and two sideband frequencies .omega..sub.rf +.omega..sub.a and .omega..sub.rf -.omega..sub.a, .omega..sub.a meaning .omega..sub.a =1/2 (.OMEGA..sub.A -.OMEGA..sub.X).
In particular, a mere sinusoidal amplitude modulation may be chosen such that the field amplitude of the composed rf field follows the function 2.gamma.hd 1B.sub.1 cos.OMEGA..sub.a t, .gamma..sub.1 B.sub.1 2.pi. meaning the amplitude of the two sidebands.
In systems with scalar couplings of the spins of the nuclei A and X to other nuclei (eg. M, k) the sideband amplitudes .gamma..sub.1 B.sub.1 /2.pi. are chosen sufficient to stir the spins of the nuclei A and X with the same nutation frequency, but to be weak enough so that the spins of all neighboring other nuclei are not affected, in particular 10 Hz.ltoreq..gamma..sub.1 B.sub.1 /2.pi..ltoreq.100 Hz, preferably .gamma..sub.1 B.sub.1 /2.pi..apprxeq.50 Hz.
If the time interval .tau..sub.m is chosen to be an integer multiple of the duration of a modulation cycle 2 .pi./.gamma..sub.1 B.sub.1, the magnetization of the nuclei A and X lies completely along the z-direction at the end of the irradiation with the composed rf field.
In a further embodiment of the method according to the present invention a composed rf field which is modulated both in amplitude and phase is irradiated. When doing so the phases of the component fields are spaced from each other by 90.degree. and their amplitudes and frequencies are chosen such that together they yield a phase-modulated rf field orthogonal to the z-axis with a carrier frequency .omega..sub.rf =1/2 (.OMEGA..sub.A +.OMEGA..sub.X) and two sideband frequencies .omega..sub.rf +.omega..sub.a and .omega..sub.rf -.omega..sub.a.
In a preferred embodiment the field amplitude of a component field follows the function .gamma..sub.1 B.sub.1 .multidot.cos.omega..sub.a t and the field amplitude of a component partial field follows the function .gamma..sub.2 B.sub.2 .multidot.cos.omega..sub.a t.multidot.cos.gamma..sub.1 B.sub.1 T. This a kind of spin-lock of the magnetization vectors I.sup.A and I.sup.X.
In order to obtain an optimal observable signal the spin-lock pulse has to be interrupted after an integer number of spin cycles of the duration 2.pi./.gamma..sub.2 B.sub.2, which can be achieved by choosing the time interval .tau..sub.m to be an integer multiple of a cycle duration 2.pi./.gamma..sub.2 B.sub.2.
With the rf field, which is modulated both in amplitude and phase in the case of scalar couplings to spins of neighboring other nuclei the field amplitude of the component fields should also be weak enough so that the spins of neighboring other nuclei are not affected, just as with the above mentioned embodiment of a mere amplitude-modulated rf field. On the other hand, the rf amplitude should be sufficient to lock the resonances of the spins of the nuclei A and X. Therefore, in a preferred embodiment, the extreme amplitudes .gamma..sub.1 B.sub.1 /2.pi. and .gamma..sub.2 B.sub.2 /2.pi. are chosen so that 10 Hz.ltoreq..gamma..sub.1 B.sub.1 /2.pi..ltoreq.100 Hz, preferably .gamma..sub.1 B.sub.1 /2.pi..apprxeq.50 Hz, and .gamma..sub.1 B.sub.1 /.gamma..sub.2 B.sub.2 .gtoreq.1, particularly .gamma..sub.1 B.sub.1 /.gamma..sub.2 B.sub.2 .apprxeq.10.
In an especially preferred embodiment the phases of all component fields are switched through 180.degree. at least once during the time interval .tau..sub.m. Thus the negative effect of an inhomogeneous broadening of the induced nutation frequencies due to non-ideal homogeneous rf fields can be minimized, which results in a refocussing of inhomogeneous dephasing.
For reasons of symmetry it is advisable to switch the phases during a time interval .tau..sub.m at an odd number and to choose the time duration .tau..sub.180 of the irradiation of the rf field with a phase switched through 180.degree. to be equal to the time duration .tau..sub.0 of the irradiation of the rf field with a phase switched through 0.degree..
In order to avoid destructive interferences, the time durations of the single intervals with switched phase are preferably chosen to be equal and an odd multiple of .tau./.omega..sub.a.
With embodiments of the present invention, the sample substance prior to irradiation of the composed rf field can be irradiated with a suitably shaped selective rf pulse sequence causing an inversion of the spin polarization of the nuclei X in relation to the nuclei A, in order to set up the defined initial condition of an anti-symmetric state=I.sub.Z.sup.A -I.sub.Z.sup.X with antiparallel spins of the nuclei A and X.
Such a selective rf pulse sequence may consist of a G.sup.3 -Gaussian cascade, as it is described in an article by L. Emsley and G. Bodenhausen in Chem. Phys. Lett. 165, 469 (1990).
Improved characteristic may be obtained with band-selective "uniform response pure phase" pulses, which are proposed by H. Geen, S. Wimperis and R. Freemann in J. Magn. Reson. 85, 620 (1989).
However, selective inversion of the spin polarization can never be perfectly realized in practice. The really-achievable antisymmetric initial state with anti-parallel spins will thus always differ from the ideal eigenstate of the system, leading to a more or less bi-exponential decay of the spins. In contrast thereto, the symmetric eigenstate .SIGMA.=I.sub.Z.sup.A +I.sub.Z.sup.X with parallel spins of the nuclei A and X always shows mono-exponential decay. With other embodiments of the present invention the symmetry is restored in that prior to irradiation of the composed rf field the sample substance is irradiated with a rf pulse sequence which excites transverse magnetization of the nuclei A and X.
Preferably the rf pulse sequence is modulated in amplitude by sin.omega..sub.a t or cos.omega..sub.a t. Thus phase-correct transverse magnetization is excited via well-defined narrow band widths.
In doing so, the 270.degree. Gaussian pulse described in an article by L. Emsley and G. Bodenhausen in J. Magn. Reson. 82, 211 (1989) may be applied as rf pulse sequences.
In case that the experimental conditions are not quite ideal the defined initial states with transverse magnetization may also be achieved in that G.sup.4 Gaussian pulse cascades are chosen as selective rf pulse sequences which are also described in the above cited article by L. Emsley and G. Bodenhausen in Chem. Phys. Lett. 165, 469 (1990).
If scalar coupling occurs between the spins of the nuclei A and X, i.e. if the scalar coupling constant J.sub.AX .noteq.0, there will be a coherent exchange of magnetization between the nuclei A and X. This will not affect the measuring results if the system at the beginning of the time interval .tau..sub.m is in a symmetric phase-equal magnetization state .SIGMA.=I.sub.Z.sup.A +I.sub.Z.sup.X, .SIGMA.'=I.sub.X.sup.A +I.sub.X.sup.X or .SIGMA."=I.sub.Y.sup.A +I.sub.Y.sup.X.
In contrast, in case of an initial state with opposite phases the observables are modulated by the scalar coupling. This modulation can simplest be separated from the slow incoherent spin exchange by Fourier transformation with respect to .tau..sub.m.
In practice it may prove simpler in consequent measurings to increment the respective time interval .tau..sub.m in integer multiples of the period of oscillation caused by the scalar coupling between the spins of the nuclei A and X.
In order to transfer the longitudinal magnetization of the nuclei A and X at the end of the irradiation with the composed rf field into an observable transverse magnetization, there are several possibilities:
In an embodiment a 270.degree. Gaussian pulse with the frequency of one of the two chemical shifts .OMEGA..sub.A or .OMEGA..sub.X is irradiated as read pulse immediately after irradiation with the composed rf field.
In a further embodiment a 270.degree. Gaussian pulse which is modulated in amplitude by the function cos.omega..sub.a t is irradiated as read pulse immediately after irradiation with the composed rf field. Thus the two nuclear resonance frequencies are simultaneously "hit".
Finally, in a further embodiment of the present invention a non-selective .pi./2 pulse may also be irradiated.
In a preferred embodiment the phase of the read pulses is alternated and combined with it the measuring signal in the detector is alternatingly added or subtracted in order to make sure that really only the remaining z-magnetization and not other transverse components are measured.
The invention will be described and explained hereafter in more detail with reference to the embodiments illustrated in the drawing. The features that can be derived from the description and the drawing may be used in other embodiments of the invention each individually or in any combination thereof.